Jan, Frank Zappa’s lyrics appear to be mostly nonsense but if you follow the lyrics of the first song, ‘Inca Roads,’ on his ‘One Size Fits All’(1975) album he appears to be saying that Chester is a space alien:

Did a booger-bear / Come from somewhere out there / Just to land in the Andes? . . . / Or did someone build a place / Or leave a space for Chester's Thing [[a flying saucer – ‘Did a vehicle / Come from somewhere out there to land’]].

There is also an implication there, I think, that the alien could take on or create various forms. Four tracks later in ‘Florentine Pogen,’ he’s talking about a girl, who is possibly one of Chester’s incarnations. He then says:

Which seems to be saying that the alien is able to change forms or create creatures that look like they are from terrestrial, but they’re not.

What this all means, who know or who cares – Zappa is all about the music and not the lyrics anyway, although he did do some satire and social commentary that appeared to be a bit more meaningful than what’s on this album!

So to answer your question, yes, there probably is some meaning to the expression, but it’s probably nonsense! (<:)

P.S. Science fiction fans, if you’re into the twilight zone, it is interesting to note that Frank Zappa, who died of cancer in 1993, wrote of Chester’s gorilla, probably an alien, in 1975, and starting in 2001 Deborah CHESTER wrote the first of her science fiction trilogy entitled ‘The Alien Chronicles,’ which was actually my first guess for the source of Chester’s gorilla!
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The real meaning of the phrase Chesters Gorilla used in Zappa songs comes from the term Booger Bear,not space aliens .
Zappas band used to pick out the band member with the ugliest groupie that night & hang a shrunken head on that band members hotel room door & it was the Booger Bear award.

Now Chesters gorilla she goes Moo is about Chester Thompson picking up a fat girl, she goes oink is Chester Thompson picking up a fat pig , she goes quack is self explainatory .

Napolean Murphy Brock would sing Cbesters Gorilla she goes ( make fart noise ) then he'd walk like his thighs were squishing together like a fat girl Chester Thompson brought back to the hotel , all the Booger Bear tom follery & Chesters Gorilla is about life in the road & the groupies Zappa & his band members picked up .

Urban dictionary tells me that a mud shark is a white woman who dates black men, usually because of low self-esteem. The same source tells me that vanilla fudge is semen mixed with faecal material. So it does seem to be referring to a rather unsavoury incident, depending on how you view these matters.

Ok the term Mud Shark is about an incident that took place at a hotel where patrons could rent fishing gear & fish from their balconys, durring the 60's & 70's many music acts all stayed at this hotel, including the rock band Vanilla Fudge .

One of the band members in Vanilla Fudge caught a few fish & had them in the hotel room bathtub & introduced a whacked out groupie to the fish , well the fish was inserted into an orifice & the Mothers happened to wittness the insertion of the fish into the females orifice & hence forth the Mud Shark was born .

Absolute true story & if you havent heard the band Vanilla Fudge you really should , an excellent rock act for that era .

Flo & Eddie from the Mothers took the Mud Shark episode they wittnessed that day & incorporeted it into their performance after Frank announced to the audience the word for the day was Mud Shark .

Oh one more piece of history is the song Suzy Creamcheese , there is a real life girl that got nicknamed Suzy Creamcheese, her real name is Pamela but i'll spare her family the embarassment of posting her last name .

I agree but most dont care about nostalgia books anymore & few writers end up with any real money from their efforts , i did author a book on a different topic & secured publishing but so many downloads of it are available for free online it soured me from further texts .